Image processing device, image processing method, and storage medium

ABSTRACT

An image processing device sets an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters, iteratively updates the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters, and executes driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.

CROSS-REFERENCE TO RELATED APPLICATION

Priority is claimed on Japanese Patent Application No. 2022-053683, filed Mar. 29, 2022, the content of which is incorporated herein by reference.

BACKGROUND Field of the Invention

The present invention relates to an image processing device, an image processing method, and a storage medium.

Description of Related Art

Conventionally, a technology of estimating a road marking on a road on which a vehicle travels and controlling the traveling of the vehicle on the basis of the estimated road marking is known. For example, Japanese Unexamined Patent Application, First Publication No. 2021-60885 discloses a technology of selecting a plurality of three-dimensional objects from an image captured by a camera mounted in a vehicle, estimating road markings on the basis of positions of the selected three-dimensional objects, and setting a target speed of the vehicle according to the curvature of the estimated road markings.

In the technology described in Japanese Patent Application, First Publication No. 2021-60885, road markings are estimated by fitting a curved line to a plurality of positions extracted from an image obtained by photographing a road on which a vehicle travels. However, in such a method, an error in the estimated road markings is large due to a restriction on a degree of freedom of the curve to be fitted, and blurring may occur in the estimated road markings due to a variation in the position extracted from the image at each time point. As a result, there are cases where the estimated road markings cannot be used stably for the traveling control of the vehicle.

SUMMARY

The present invention has been made in consideration of such circumstances, and an object thereof is to provide an image processing device, an image processing method, and a storage medium capable of estimating road markings that can be stably used for traveling control of a mobile object.

An image processing device, an image processing method, and a storage medium according to the present invention have adopted the following configurations.

: An image processing device according to one aspect of the present invention includes a storage medium configured to store an instruction readable by a computer and a processor that is connected to the storage medium, in which the processor executes an instruction readable by the computer, thereby setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters, iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters, and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.

(2): In the aspect of (1) described above, the function is a quadratic function, the hardware processor sets an initial value of a linear coefficient of the quadratic function on the basis of an identification value of the road boundary recognized in a lateral direction of the image, and the hardware processor iteratively updates the parameters at a predetermined time point by setting forgetting gains of secondary coefficients and the linear coefficients of the parameters at the previous time point to the predetermined time point to values smaller than 1.

(3): In the aspect of (1) described above, the hardware processor iteratively updates parameters of a function that approximates a road boundary by dividing the image at predetermined intervals, iteratively updating the parameters of the function that approximates the road boundary for each divided area, and combining the parameters.

(4): In the aspect of (1) described above, the hardware processor uses a learned model learned to output a probability value indicating an existence probability of a road boundary for each of coordinates of the image in response to an input of the image to acquire the probability value and update the parameters on the basis of the probability value and the coordinates.

(5): In the aspect of (4) described above, the hardware processor iteratively updates the parameters to minimize an error between a component of the coordinates in a first direction and an estimated value of the component in the first direction calculated on the basis of a component of the coordinates in a second direction.

(6): An image processing method according to another aspect of the present invention includes, by a computer, setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters, iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters, and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.

(7): A computer-readable non-transitory storage medium according to still another aspect of the present invention stores a program causing a computer to execute setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters, iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters, and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.

According to (1) to (7), it is possible to estimate road markings that can be stably used for traveling control of a mobile object.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram which shows an example of an environment in which an image processing device mounted in a host vehicle M is used.

FIG. 2 is a diagram which shows an example of a configuration of the image processing device.

FIG. 3 is a diagram which shows an example of a method in which a candidate point extraction unit extracts candidate points on a track boundary.

FIG. 4 is a diagram which shows an example of a method for rearranging candidate points on a track boundary.

FIG. 5 is a diagram for describing an outline of a track boundary model updated by a model parameter updating unit.

FIG. 6 is a diagram which shows an example of a flow of model parameter update processing executed by a model parameter updating unit.

FIG. 7 is a graph for describing a method of calculating a reference value of a model parameter.

FIG. 8 is a sequence diagram which shows an example of a flow of processing executed by the image processing device.

DESCRIPTION OF EMBODIMENT

Hereinafter, embodiments of an image processing device, an image processing method, and a storage medium of the present invention will be described with reference to the drawings. In the present embodiment, the image processing device is, for example, a terminal device such as a smartphone having a camera and a display. However, the present invention is not limited to such a configuration, and the image processing device may be a computer device as long as it receives at least an image captured by a camera, processes it, and outputs a result of the processing to a display. In this case, functions of the present invention are realized by the camera, the display, and the image processing device in cooperation.

Configuration

FIG. 1 is a diagram which shows an example of an environment in which an image processing device 100 mounted in a host vehicle M is used. The host vehicle M is, for example, a two-wheeled, three-wheeled, or four-wheeled vehicle, and its drive source is an internal combustion engine such as a diesel engine or a gasoline engine, an electric motor, or a combination thereof. The electric motor operates using electric power generated by a generator connected to the internal combustion engine, or electric power discharged from a secondary battery or a fuel cell.

As shown in FIG. 1 , the image processing device 100 is installed in the host vehicle M so that the camera 10 can capture an image of an area in front of the host vehicle M in a traveling direction. The image processing device 100 is held by, for example, an in-vehicle holder (not shown) attached to a dashboard of the host vehicle M, and captures an image of the area in front of the host vehicle M. The host vehicle M is an example of a “mobile object.” In the following description, in the present embodiment, an example in which the image processing device 100 is mounted in the host vehicle M, which is a mobile object, is described, but more generally, the mobile object includes devices with cameras mounted in a vehicle such as dash cameras and smartphones.

FIG. 2 is a diagram which shows an example of a configuration of the image processing device 100. As shown in FIG. 2 , the image processing device 100 includes, for example, a camera 10, a display unit 20, a candidate point extraction unit 110, a model parameter updating unit 120, and a driving control unit 130. The candidate point extraction unit 110, the model parameter updating unit 120, and the driving control unit 130 are realized by a hardware processor such as a central processing unit (CPU) executing a program (software). Some or all of these components may be realized by hardware (a circuit unit; including circuitry) such as large scale integration (LSI), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), and a graphics processing unit (GPU) or by software and hardware in cooperation. The program may be stored in advance in a storage device (a storage device having a non-transitory storage medium) such as a hard disk drive (HDD) or flash memory, or may be stored in a removable storage medium (a non-transitory storage medium) such as a DVD or CD-ROM and may be installed by the storage medium being attached to a drive device. The camera 10 is, for example, a digital camera using a solid-state imaging device such as a charge coupled device (CCD) or complementary metal oxide semiconductor (CMOS). The display unit 20 is, for example, a display device such as a touch panel or liquid crystal display.

Extraction of Candidate Point

The candidate point extraction unit 110 extracts candidate points of a boundary of a track (a track boundary) on which the host vehicle M travels on the basis of an image representing the area in front of the host vehicle M captured by the camera 10. FIG. 3 is a diagram which shows an example of a method in which the candidate point extraction unit 110 extracts candidate points on a track boundary. As shown in FIG. 3 , when the candidate point extraction unit 110 acquires an image captured by the camera 10, it inputs the acquired image into a learned model (deep neural network; DNN) that has been learned to output a probability value (0 or more and 1 or less) indicating whether each pixel (coordinates) of the image is a track boundary according to the input of the image. The candidate point extraction unit 110 extracts pixels for which the output probability values take positive values as candidate points of the track boundary. Alternatively, the candidate point extraction unit 110 may also extract pixels for which the output probability values are equal to or greater than a threshold value (for example, 0.5) as candidate points of the track boundary.

Update of Model Parameter

The model parameter updating unit 120 rearranges the candidate points of the track boundary extracted by the candidate point extraction unit 110 in descending order of the probability value, and uses the candidate points of the track boundary in descending order of the probability value to update model parameters of a track boundary model to be described below. FIG. 4 is a diagram which shows an example of a method of rearranging the candidate points of a track boundary. In FIG. 4 , k indicates a time point in a recognition cycle for recognizing a track boundary, N(k) indicates the number of candidate points of the track boundary acquired at the time point k, x′ (n,k) indicates an x-coordinate of each candidate point before rearrangement, y′(n,k) indicates a y-coordinate of each candidate point before rearrangement, x(n,k) indicates an x-coordinate of each candidate point after rearrangement, and y(n,k) indicates a y-coordinate of each candidate point after rearrangement. As will be described below, by iteratively updating the model parameters of the track boundary model using the candidate points of the track boundary in descending order of the probability value, even if down-sampling occurs within one recognition cycle, it is possible to output a track boundary model with high accuracy even in a shorter time.

FIG. 5 is a diagram for describing an outline of the track boundary model updated by the model parameter updating unit 120. The model parameter updating unit 120 obtains an estimated value y_(_hat)(n,k) of the track boundary by iteratively substituting the candidate points of the track boundary rearranged in descending order of the probability value into the track boundary model defined by the following Equation (1).

$\begin{matrix} {y_{\_ hat}\left( \text{n,k} \right)\begin{array}{l} {= {\sum\limits_{\text{i=1}}^{\text{m}}w_{\text{i}}}\left( {x\left( \text{n,k} \right)} \right)\left( {a_{\text{i}}\left( \text{n,k} \right)x\left( \text{n,k} \right)^{2} + b_{\text{i}}\left( \text{n,k} \right)x\left( \text{n,k} \right) + c_{\text{i}}\left( \text{n,k} \right)} \right)\quad\left( \text{i=1\textasciitilde m} \right)} \\ {= {\sum\limits_{\text{i=1}}^{\text{m}}w_{\text{i}}}\left( {x\left( \text{n,k} \right)} \right)\theta_{\text{i}}\left( \text{n,k} \right)^{\text{T}}\zeta\left( \text{n,k} \right)} \\ {= {\sum\limits_{\text{i=1}}^{\text{m}}w_{\text{i}}}\left( {x\left( \text{n,k} \right)} \right)y_{\_ hat\_\text{i}}\left( \text{n,k} \right)} \\ {= \theta_{\text{i}}\left( \text{n,k} \right)^{\Gamma}\zeta\left( \text{n,k} \right)} \end{array}} & \text{­­­Equation (1)} \end{matrix}$

In Equation (1), a_(i)(n,k), b_(i)(n,k), and c_(i)(n,k) represent a second order coefficient, a first order coefficient, and a constant term of a quadratic function (which may be referred to hereinafter as an “element function”) that approximates a track boundary in an image, respectively, and w_(i) represents a weighting function that outputs a weight of 0 or more and 1 or less according to an x-coordinate of the input candidate point. More specifically, the weighting function is defined by the following Equations (2) to (4). In Equations (2) to (4), the values of x_(wi) (i=1 to m) are fixed values set in advance. A sum of w_(i)(x) (i=1 to m) is set to always be one.

$\begin{matrix} {w_{1}(x) = \left\{ \begin{array}{ll} 1 & \left( {x\left( \text{k} \right)\underline{\leq}x_{w1}} \right) \\ \frac{x_{w2} - x\left( \text{k} \right)}{x_{w2} - x_{w1}} & {\left( {x_{w1} < x\left( \text{k} \right) < x_{w2}} \right)\text{­­­Equation (2)}\left( {\text{i} = 1} \right)} \\ 0 & \left( {x_{w2}\underline{\leq}x\left( \text{k} \right)} \right) \end{array} \right)} &  \end{matrix}$

$\begin{matrix} {w_{\text{i}}(x) = \left\{ \begin{array}{ll} 0 & \left( {x\left( \text{k} \right)\underline{\leq}x_{w\text{i-1}}} \right) \\ \frac{x\left( \text{k} \right)\text{-}x_{w\text{i-1}}}{x_{w\text{i}} - x_{w\text{i-1}}} & \left( {x_{w\text{i-1}} < x\left( \text{k} \right)\underline{\leq}x_{w\text{i}}} \right) \\ \frac{w_{w\text{i+1}} - x\left( \text{k} \right)}{x_{w\text{i+1}} - x_{w\text{i}}} & \left( {x_{w\text{i}} < x\left( \text{k} \right) < x_{w\text{i+1}}} \right) \\ 0 & \left( {x_{w\text{i+1}}\underline{\leq}x\left( \text{k} \right)} \right) \end{array} \right)\left( \text{i=2\textasciitilde m-1} \right)} & \text{­­­Equation (3)} \end{matrix}$

$\begin{matrix} {w_{\text{m}}(x) = \left\{ \begin{array}{ll} 0 & \left( {x\left( \text{k} \right)\underline{\leq}x_{w\text{m-1}}} \right) \\ \frac{x\left( \text{k} \right) - x_{w\text{m-1}}}{x_{w\text{m}} - x_{w\text{m-1}}} & {\left( {x_{w\text{m-1}} < x\left( \text{k} \right) < x_{w\text{m}}} \right)\text{­­­Equation (4)}\left( {\text{i} = \text{m}} \right)} \\ 1 & \left( {x_{w\text{m}}\underline{\leq}x\left( \text{k} \right)} \right) \end{array} \right)} &  \end{matrix}$

FIG. 5 shows element functions f₁, f₂, f₃ and weighting functions w₁, w₂, w₃ when m=3 in equations (1) to (4). That is, the track boundary model in the present embodiment divides an image into a plurality of areas based on the x-coordinate, approximates a track boundary by a quadratic function for each divided area, and approximates the track boundary in the entire image by combining the quadratic function for each area.

In this manner, compared to a conventional method (a least-squares method of a batch calculation method) in which the candidate points of a track boundary in an image are approximated by a single quadratic function, the track boundary is approximated by a quadratic function for each partial area of the image, and the approximated quadratic functions are combined to obtain a final approximation curve in the present embodiment, so that the track boundary in the image can be expressed with higher accuracy.

Note that, in the present embodiment, values and the number of x-coordinates x_(wi) (i=1 to m) for dividing the area are fixed values set in advance. However, the present invention is not limited to such a configuration, and the values and number of x-coordinates x_(wi) for dividing the area may be set as, for example, the number of clusters obtained by clustering the extracted candidate points and boundary points thereof.

Next, model parameter update processing executed by the model parameter updating unit 120 will be described with reference to FIG. 6 . FIG. 6 is a diagram which shows an example of a flow of the model parameter update processing executed by the model parameter updating unit 120.

First, the model parameter updating unit 120 rearranges the candidate points (x′(n,k) and y′(n,k)) of the track boundary extracted by the candidate point extraction unit 110 in descending order of the probability value, and obtains candidate points (x(n,k) and y(n,k)). The model parameter updating unit 120 generates a vector ξ(n,k)=[x(n,k)²,x(n,k),1] based on the candidate point x(n,k), and substitutes x(n,k) into the weighting function w_(i) to obtain a weighting value w_(i)(x(n,k)).

Next, the model parameter updating unit 120 calculates an inner product of the vetor ξ(n,k) and model parameters θ_(i)(n,k)=[a_(i)(n,k),b_(i)(n,k),c_(i)(n,k)] and multiplies it by the weighting value w_(i)(x(n,k)), thereby obtaining element functions f_(i)(x)=w_(i)(x(n,k))(a_(i)(n,k)×(n,k)²+b_(i)(n,k)×(n,k)+c_(i)(n,k)) for each area. The model parameter updating unit 120 obtains an output estimated value y_(_hat)(n,k) represented by Equation (1) by taking a sum of the elemental functions f_(i)(x) for each area. Initial values of the model parameters θ_(i)(n,k)=[a_(i)(n,k),b_(i)(n,k),c_(i)(n,k)] to be multiplied at this time will be described below.

The model parameter updating unit 120 then calculates an identification error between the output estimated value y_(_hat)(n,k) and a y-coordinate y(n,k) of a candidate point as e_(id)(n,k)=w_(i)(x(n,k))(y(n,k)-y_(_hat)(n,k)). The identification error can be reflected for each area by multiplying the error between the output estimated value y_(_hat)(n,k) and the y-coordinate y(n,k) of the candidate point by the weighting value w_(i)(x(n,k)). The model parameter updating unit 120 defines an adaptive gain K_(p) for correcting the model parameter θ_(i)(n,k) in a direction of decreasing a squared error of the identification error e_(id)(n,k) by the following Equation (5).

$\begin{matrix} {K_{p}\left( \text{n,k} \right) = \frac{P^{\prime}\left( \text{n-1,k} \right)\zeta\left( \text{n,k} \right)}{1 + \zeta\left( \text{n,k} \right)^{\text{T}}P^{\prime}\left( \text{n-1,k} \right)\zeta\left( \text{n,k} \right)}} & \text{­­­Equation (5)} \end{matrix}$

In Equation (5), P′(n,k) represents a covariance matrix of 3 rows and 3 columns and is a matrix defined by Equation (6) below.

$\begin{matrix} {P^{\prime}\left( \text{n,k} \right) = \frac{1}{\lambda_{1}}\left( {\text{I} - \frac{\lambda_{2}P^{\prime}\left( \text{n-1,k} \right)\zeta\left( \text{n,k} \right)\zeta\left( \text{n,k} \right)^{\text{T}}}{\lambda_{1} + \lambda_{2}\zeta\left( \text{n,k} \right)^{\text{T}}P^{\prime}\left( \text{n-1,k} \right)\zeta\left( \text{n,k} \right)}} \right)P^{\prime}\left( \text{n-1,k} \right)} & \text{­­­Equation (6)} \end{matrix}$

In Equation (6), I represents a unit matrix of 3 rows and 3 columns, and λ₁ and λ₂ represent setting parameters of an iterative identification algorithm. λ₁ and λ₂ are constant values greater than 0 and equal to or less than 1. They are set as λ₁=1 and λ₂=1 when a least squares method is applied, set as λ₁=λ(0<λ≤1) 1 and λ₂=1 when a weighted least squares method is applied, and set as λ₁=1 and λ₂=0 when a fixed gain method is applied. When the fixed gain method is applied, the adaptive gain K_(p) is represented by the following Equations (7) and (8).

$\begin{matrix} {K_{p}\left( \text{n,k} \right) = \frac{P\zeta\left( \text{n,k} \right)}{1 + \zeta\left( \text{n,k} \right)^{\text{T}}P\zeta\left( \text{n,k} \right)}} & \text{­­­Equation (7)} \end{matrix}$

$\begin{matrix} {P = \begin{bmatrix} P_{1} & 0 & 0 \\ 0 & p_{2} & 0 \\ 0 & 0 & p_{3} \end{bmatrix}} & \text{­­­Equation (8)} \end{matrix}$

In Equation (8), P represents an identification gain matrix. P₁, P₂, and P₃ represent identification gains and are positive fixed values. The model parameter updating unit 120 multiplies the identification error e_(id)(n,k) by the adaptive gain K_(p), thereby obtaining a correction amount ddθ_(i)(n,k) of the model parameter represented by the following equation (9).

$\begin{matrix} {dd\theta_{\text{i}}\left( \text{n,k} \right) = K_{p}\left( \text{n,k} \right)e_{id\_\text{i}}\left( \text{n,k} \right)\quad\left( \text{i=1\textasciitilde m} \right)} & \text{­­­Equation (9)} \end{matrix}$

Next, the model parameter updating unit 120 multiplies a previous value dθ (n-1,k) of the final correction amount, which will be described below, by a forgetting gain Δ_(fgt), and adds the obtained multiplied value to the correction amount ddθ_(i)(n,k) of the model parameter of Equation (9), thereby obtaining a correction amount dθ_(raw_i)(n,k) of the model parameter represented by the following Equation (10). In this manner, by defining the correction amount dθ_(raw_i)(n,k) using a value obtained by multiplying the final correction amount dθ_(i)(n-1,k) previously obtained by the forgetting gain Δ_(fgt), abrupt fluctuations of the track boundary model can be curbed.

$\begin{matrix} {d\theta_{raw\_\text{i}}\left( \text{n,k} \right) = \Delta_{fgt}d\theta_{\text{i}}\left( \text{n-1,k} \right) + K_{p}\left( \text{n,k} \right)e_{id\_\text{i}}\left( \text{n,k} \right)} & \text{­­­Equation (10)} \end{matrix}$

In Equation (10), the forgetting gain Δ_(fgt) is a diagonal matrix of 3 rows and 3 columns represented by the following Equation (11). In Equation (11), δ_(fgt_1), δ_(fgt_2), and δ_(fgt_3) are constant values that satisfy 0<δ_(fgt_1), δ_(fgt_2)<1, and δ_(fgt_3)=1. That is, the forgetting gain Δ_(fgt) is set to apply a forgetting effect to a_(i)(n,k) and b_(i)(n,k).

$\begin{matrix} {\Delta_{fgt} = \begin{bmatrix} \delta_{fgt\_ 1} & 0 & 0 \\ 0 & \delta_{fgt\_ 2} & 0 \\ 0 & 0 & \delta_{fgt\_ 3} \end{bmatrix}} & \text{­­­Equation (11)} \end{matrix}$

Next, the model parameter updating unit 120 performs limiter processing (an example of a “constraint condition”) represented by the following Equations (12) to (14) on the correction amount dθ_(raw_i)(n,k) of the model parameter to correct the correction amount of the model parameter and obtain a final correction amount dθ_(i)(n,k) represented by the following Equation (15). In Equations (12) to (14), da_(L), da_(H), db_(L), db_(H), dc_(L), and dc_(H) are fixed values set in advance, and are set to prevent the track boundary model from being in an unrealistic shape.

$\begin{matrix} {da_{\text{i}}\left( \text{n,k} \right) = \left\{ \begin{array}{ll} {da_{L}\left( \text{n,k} \right)} & \left( {da_{raw\_\text{i}}\left( \text{n,k} \right) < da_{L}} \right) \\ {da_{raw\_\text{i}}\left( \text{n,k} \right)} & \left( {da_{L}\underline{\leq}da_{raw\_\text{i}}\left( \text{n,k} \right)\underline{\leq}da_{H}} \right) \\ {da_{H}\left( \text{n,k} \right)} & \left( {da_{H} < da_{raw\_\text{i}}\left( \text{n,k} \right)} \right) \end{array} \right)} & \text{­­­Equation (12)} \end{matrix}$

$\begin{matrix} {db_{\text{i}}\left( \text{n,k} \right) = \left\{ \begin{array}{ll} {db_{L}\left( \text{n,k} \right)} & \left( {db_{raw\_\text{i}}\left( \text{n,k} \right) < db_{L}} \right) \\ {db_{raw\_\text{i}}\left( \text{n,k} \right)} & \left( {db_{L}\underline{\leq}db_{raw\_\text{i}}\left( \text{n,k} \right)\underline{\leq}db_{H}} \right) \\ {db_{H}\left( \text{n,k} \right)} & \left( {db_{H} < db_{raw\_\text{i}}\left( \text{n,k} \right)} \right) \end{array} \right)} & \text{­­­Equation (13)} \end{matrix}$

$\begin{matrix} {dc_{\text{i}}\left( \text{n,k} \right) = \left\{ \begin{array}{ll} {dc_{L}\left( \text{n,k} \right)} & \left( {dc_{raw\_\text{i}}\left( \text{n,k} \right) < dc_{L}} \right) \\ {dc_{raw\_\text{i}}\left( \text{n,k} \right)} & \left( {dc_{L}\underline{\leq}db_{raw\_\text{i}}\left( \text{n,k} \right)\underline{\leq}dc_{H}} \right) \\ {dc_{H}\left( \text{n,k} \right)} & \left( {dc_{H} < dc_{raw\_\text{i}}\left( \text{n,k} \right)} \right) \end{array} \right)} & \text{­­­Equation (14)} \end{matrix}$

$\begin{matrix} {d\theta_{\text{i}}\left( \text{n,k} \right) = \begin{bmatrix} {da_{\text{i}}\left( \text{n,k} \right)} \\ {db_{\text{i}}\left( \text{n,k} \right)} \\ {dc_{i}\left( \text{n,k} \right)} \end{bmatrix}} & \text{­­­Equation (15)} \end{matrix}$

Next, the model parameter updating unit 120 adds a reference value θ_(base_i)(n,k) of the model parameter represented by the following Equation (16) to the correction amount dθ_(i)(n,k), thereby obtaining a current model parameter value θ_(i)(n,k) represented by the following Equation (17). The calculated current model parameter value θ_(i)(n,k) is used as an identification value (an initial value) for calculating the model parameter θ_(i)(n+1,k) for a next input value n+1.

$\begin{matrix} {\theta_{base\text{\_i}}\left( \text{n,k} \right) = \begin{bmatrix} {a_{base\text{\_i}}\left( \text{n,k} \right)} \\ {b_{base\text{\_i}}\left( \text{n,k} \right)} \\ {c_{base\_ i}\left( \text{n,k} \right)} \end{bmatrix}} & \text{­­­Equation (16)} \end{matrix}$

$\begin{matrix} {\theta_{\text{i}}\left( \text{n,k} \right) = \theta_{base\_\text{i}}\left( \text{n,k} \right) + d\theta_{i}\left( \text{n,k} \right)} & \text{­­­Equation (17)} \end{matrix}$

Reference Value Calculation of Model Parameter

Next, a method for calculating the reference value θ_(base_i)(n,k) of the model parameter will be described with reference to FIG. 7 . FIG. 7 is a graph for describing a method of calculating a reference value of the model parameter. The model parameter updating unit 120 sets the reference value θ_(base_i)(n,k) of the model parameter using the following Equations (18) to (20).

$\begin{matrix} {a_{base\text{\_i}}\left( \text{n,k} \right) = 0} & \text{­­­Equation (18)} \end{matrix}$

$\begin{matrix} {c_{base\text{\_i}}\left( \text{n,k} \right) = 0} & \text{­­­Equation (19)} \end{matrix}$

$\begin{matrix} {b_{base\text{\_i}}\left( \text{n,k} \right)\begin{array}{l} {= g\left( {c_{\text{i}}\left( \text{n-1,k} \right)} \right)} \\ {= \alpha c_{\text{i}}\left( \text{n-1,k} \right) + \beta} \end{array}} & \text{­­­Equation (20)} \end{matrix}$

Equations (18) and (19) represent initial values of model parameters a_(base_i)(n,k) and c_(base_i)(n,k), respectively. As shown in Equations (18) and (19), since the track boundary model can be curved in both left and right directions, the initial value of the model parameter a_(base_i)(n,k) may be zero, and since a model parameter c_(i) corresponding to a y-intercept of the track boundary model can be in both left and right directions, the initial value of the model parameter c_(base_i)(n,k) may be zero.

In Equation (20), c_(i)(n-1,k) represents a previously calculated identification value of the model parameter c_(i), and a function g represents a scaling function that gives a straight line passing through the identification value (that is, the y-intercept) of the model parameter c_(i) and a vanishing point VP of an image. That is, as shown in a left part of FIG. 7 , as the identification value c_(i)(n-1,k) takes a larger value, the reference value b_(base_i)(n,k) of the model parameter takes a smaller value, and, as shown in a right part of FIG. 7 , the straight line inclines to the left. By setting the reference value θ_(base_i)(n,k) of the model parameter using the methods described above, it is possible to prevent the track boundary model from being in an unrealistic shape even when the number of DNN output values N(k) in a certain recognition cycle is extremely small due to, for example, an event such as bad weather or dark visibility conditions.

When the model parameter updating unit 120 determines a track boundary model for each recognition cycle, the driving control unit 130 performs automated driving or driving assistance of the host vehicle M on the basis of the determined track boundary model. More specifically, for example, the driving control unit 130 performs bird’s-eye view conversion on a track boundary model in a camera coordinate system to obtain a track boundary model in a bird’s-eye view coordinate system. The driving control unit 130 generates a target trajectory and an action plan of the host vehicle M using the track boundary model in the bird’s-eye view coordinate system, and causes the host vehicle M to travel according to the generated target trajectory and action plan. In addition, for example, the driving control unit 130 uses the track boundary model in the bird’s-eye view coordinate system to assist with steering or to issue a warning such that the host vehicle does not deviate from the determined track boundary model when an occupant of the host vehicle M performs manual driving.

FIG. 8 is a sequence diagram which shows an example of a flow of processing executed by the image processing device 100. As shown in FIG. 8 , at a time point k-2, the image processing device 100 rearranges DNN output values x′(1,k-2), y′(1,k-2), x′(2,k-2 ), y′(2,k-2), ..., x′(N(k-2),k-2)), y′(N(k-2),N(k-2)) in descending order of the probability value, and obtains x(1,k-2), y(1,k-2), x(2,k-2), y(2,k-2),..., x(N(k-2), k-2), and y(N(k-2), k-2). The image processing device 100 constitutes a vector ξ(n,k-2)=[x(n,k-2)²,x(n,k-2),1] in descending order of the probability value, and inputs it to the iterative identification algorithm as shown in FIG. 6 to iteratively update the model parameter values θ_(i)(n,k-2).

When a resampling timing T_(ds) has elapsed while the model parameter value θ_(i)(n,k-2) is being updated, the image processing device 100 performs down-sampling on a model parameter value (for example, θ_(i)(N(k-2)-1,k-2)) at a time when the resampling timing T_(ds) has elapsed, and determines the result as the final model parameter value in a recognition cycle k-2. The image processing device 100 causes the display unit 20 to display a track boundary model set with the determined model parameter value θ_(i)(N(k-2)-1,k-2). As described above, unlike the least-squares method of the batch calculation method, in the present embodiment, the model parameter value θ_(i)(n,k) is iteratively updated by using the output values in descending order of the probability value, thereby it is possible to estimate a track boundary model with high accuracy even when the data amount is large and calculation cannot be completed by the least-squares method of the batch calculation method.

The image processing device 100, in a recognition cycle k-1, rearranges DNN output values x′(1,k-1), y′(1,k-1), x′(2,k-1), y′(2,k-1), ..., x′(N(k-1),k- 1), y′(N(k-1),k-1) in descending order of the probability value, and obtains x(1,k-1), y(1,k-1), x(2,k-1), y(2,k-1), ..., x(N(k-1),k-1), and y(n(k-1),k-1). The image processing device 100 constitutes a vector ξ(n,k-1)=[x(n,k-1)²,×(n,k-1), 1] in descending order of the probability value, and updates the model parameter value θ_(i)(n,k-1) by inputting it to the iterative identification algorithm as shown in FIG. 6 . At this time, the image processing device 100 uses the model parameter value θ_(i)(N(k-2)-1,k-2)) determined in a recognition cycle k-2, as an initial value for calculating the estimated value y__(hat)(1,k-1). When the model parameter value θ_(i)(n,k-1) has been updated to the output values of x(N(k-1),k-1) and y(N(k-1),k-1), the image processing device 100 holds the model parameter value θ_(i)(N(k-1),k-1) until a next recognition cycle k, and causes the display unit 20 to display a track boundary model with the held model parameter value θ_(i)(N(k-1),k-1) set. Thereafter, in the recognition cycle k, the image processing device 100 similarly updates the model parameter value θ_(i)(n,k) by using DNN output values x′(1,k), y′(1,k), x′(2,k), y′(2,k), ..., x′(N(k),k), and y′(N(k),k). At this time, the image processing device 100 uses the model parameter value θ_(i)(N(k-1),k-1) determined in the recognition cycle k-1 as an initial value for calculating the estimated value y_(_hat)(1,k).

According to the present embodiment described above, the image processing device divides an area in front of a host vehicle on a coordinate system based on the host vehicle at predetermined intervals, generates a function for approximating a road marking in each area on the basis of a probability value indicating an existence probability of the road marking for each of coordinates in each area obtained by the division and corresponding coordinates, and generates a function that approximates a road marking in the front area by combining the functions generated for each area. As a result, it is possible to estimate road markings that can be stably used for traveling control of mobile objects.

The embodiment described above can be expressed as follows.

An image processing device includes a storage medium that stores an instruction readable by a computer and a processor that is connected to the storage medium, in which the processor executes an instruction readable by the computer, thereby setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters, iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters, and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.

As described above, a mode for implementing the present invention has been described using the embodiments, but the present invention is not limited to such embodiments at all, and various modifications and replacements can be added within a range not departing from the gist of the present invention. 

What is claimed is:
 1. An image processing device comprising: a storage medium configured to store an instruction readable by a computer and a processor that is connected to the storage medium, wherein the processor executes the instruction readable by the computer, thereby setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters; iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters; and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.
 2. The image processing device according to claim 1, wherein the function is a quadratic function, the hardware processor sets an initial value of a linear coefficient of the quadratic function on the basis of an identification value of the road boundary recognized in a lateral direction of the image, and the hardware processor iteratively updates the parameters at a predetermined time point by setting forgetting gains of secondary coefficients and the linear coefficients of the parameters at the previous time point to the predetermined time point to values smaller than
 1. 3. The image processing device according to claim 1, wherein the hardware processor iteratively updates parameters of a function that approximates a road boundary by dividing the image at predetermined intervals, iteratively updating the parameters of the function that approximates the road boundary for each divided area, and combining the parameters.
 4. The image processing device according to claim 1, wherein the hardware processor uses a learned model learned to output a probability value indicating an existence probability of a road boundary for each of coordinates of the image in response to an input of the image to acquire the probability value and update the parameters on the basis of the probability value and the coordinates.
 5. The image processing device according to claim 4, wherein the hardware processor iteratively updates the parameters to minimize an error between a component of the coordinates in a first direction and an estimated value of the component in the first direction calculated on the basis of a component of the coordinates in a second direction.
 6. An image processing method comprising: by a computer, setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters; iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters; and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters.
 7. A computer-readable non-transitory storage medium that stores a program causing a computer to execute: setting an initial value of at least one of parameters of a function that approximates a road boundary in an image representing an area in front of a mobile object, captured by a camera mounted on the mobile object, on the basis of identification values of other parameters among the parameters, iteratively updating the parameters at a predetermined time point on the basis of the parameters at a previous time point to the predetermined time point and constraint conditions set for the parameters, and executing driving control or driving assistance of the mobile object on the basis of the road boundary approximated by the function that has the updated parameters. 